Cylinder and Its Surface Area

Q.

The curved surface area of a right circular cylinder of height $14cm$ is $88c{m}^2$. Find the diameter of the base of the cylinder. (Assume $\mathrm{\pi }=\frac{22}{7}$)

Q.

A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of cloth required to make the tent at the rate of Rs 80 per square metre. $[Take\pi =\frac{22}{7.}]$

Q.

Mayank made a birdbath for his garden in the shape of a cylinder with a hemispherical depression at one end (see Fig.). The height of the cylinder is $1.45m$ and its radius is $30cm$. Find the total surface area of the birdbath. (Take $\pi$ = $\frac{22}{7}$)

Q.

A toy is in the form of a cylinder with hemispherical ends. If the whole length of the toy is 90 cm and its diameter is 42 cm, find the cost of painting the toy at the rate of 70 paise per sq cm.

Q.

A circus tent is cylindrical to a height of 4m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of canvas required is

(a) $1760m^2$ (b) $2640m^2$

(c) $3960m^2$ (d) $7920m^2$

Q.

The total surface area of a cylinder whose radius is $4cm$ and height is $10cm$ is _____ $c{m}^2$

Q.

A cylindrical can whose base is horizontal and of radius 3.5 cm contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can,

Calculate:
(i) the total surface area of the can in contact with water when the sphere is in it.
(ii) the depth of water in the can before the sphere was put into the can.

Take π as ²²/₇ and give your answers as proper fractions.

1. 188.50 cm², 9/4 cm

2. 192.50 cm², 7/3 cm

3. 192.50 cm², 8/3 cm

4. 192.50 cm², 9/4 cm

5. 185.50 cm², 7/3 cm

6. 185.50 cm², 8/3 cm

7. 185.50 cm², 9/4 cm

8. 188.50 cm², 7/3 cm

9. 188.50 cm², 8/3 cm

Q. If the perimeter of a circle is equal to that of square, then the ratio of their areas is:

1. 22:7
2. 14:11
3. 7:22
4. 11:14

Q.

The surface area of a solid sphere is increased by 21% without changing it's shape. Find the percentage increase in its:

I)radius

2) volume

Q.

The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is

(a) 2 : 1 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1

Q.

A cylindrical pencil sharpened at one edge is the combination of

(a) a cylinder and a cone

(b) a cylinder and frustum of a cone

(c) a cylinder and a hemisphere

(d) two cylinders

Q. A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire.

Q.

The total surface area of a hollow metal cylinder, open at both ends, of external radius $8cm$ and height $10cm$ is $338\pi c{m}^2.$ Taking $r$ to be inner radius, write down an equation in $r$ and use it to state the thickness of the metal.

1. $3cm$

2. $4cm$

3. $1.5cm$

4. $2cm$

Q. The curved surface area of a sphere is 5544 cm². Find its volume.

Q.

The diameter of a cylinder is 28 cm and its height is 20 cm. The total surface area of the cylinder is

(a) 2993 $c{m}^2$ (b) 2992 $c{m}^2$ (c) 2292 $c{m}^2$ (d) 2229 $c{m}^2$

Q. 50 circular plates, each of diameter 14 cm and thickness 0.5 cm, are placed one above the other to form a right circular cylinder. Find its total surface area.

1. 1388 $c{m}^2$
2. 1408 $c{m}^2$
3. 1500 $c{m}^2$
4. 1550 $c{m}^2$

Q.

A funnel is the combination of

(a) a cylinder and a cone

(b) a cylinder and a hemisphere

(c) a cylinder and frustum of a cone

(d) a cone and a hemisphere

Q. The ratio of lateral surface area to the total surface area of a cylinder with base diameter 1.6 m and height 20 cm is

(a) 1 : 7

(b) 1 : 5

(c) 7 : 1

(d) 8 : 1

Q.

The volume of a solid cylinder is ${\text{448π cm}}^3$ and height $7\text{cm}$. Find its lateral surface area and total surface area ?

Q.

The outer and inner diameters of a circular ring are 34 cm and 32 cm respectively. The area of the ring is:

1. 66 π cm²

2. 33 π cm²

3. 29 π cm²

4. 60 π cm²

Q. The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is

(a) 3 cm

(b) 4 cm

(c) 6 cm

(d) 12 cm

Q. The volume of a sphere is 4851 cm³. Find its curved surface area.

Q. The radii of the ends of a bucket 16 cm height are 20 cm and 8 cm. The curved surface area of the bucket is

(a) 1760 cm²

(b) 2240 cm²

(c) 880 cm²

(d) 3120 cm²

Q. If four times the sum of the areas of two circular faces of a cylinder of height 8 cm is equal to twice the curve surface area, then diameter of the cylinder is

(a) 4 cm

(b) 8 cm

(c) 2 cm

(d) 6 cm

Q. Prove that the surface area of a sphere is equal to the curved surface area of the circumscribed cylinder.

Q. The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.

Q.

A cylindrical can, whose base is horizontal and of radius 3.5 cm, contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can, calculate :
(i) the total surface area of the can in contact with water when the sphere is in it;
(ii) the depth of water in the can before the sphere was put into the can.

Q.

The largest possible sphere is carved out from a cube of 7 cm side. The volume of the sphere will be

1. 185 cm³

2. 179.66 cm³

3. 145 cm³

4. 125.55 cm³

Q.

Find the volume of the sphere whose radius is 3 cm.

Q.

The radius of the circular base of a cylinder is 14 cm and height is 10 cm. Calculate the curved surface area of the cylinder.